5 citations · 7 across the 6 of their papers we have counts for
9 papers
Primeless proofs of the Menger and Rothberger games
Renan Maneli Mezabarba
We continue the study of the Menger and Rothberger games on lattices carried out in "Pointless proofs of the Menger and Rothberger games" (Topology Appl. 300 (2021), 107774). This…
Existence of bases implies the axiom of choice, a foundation-free proof
Gabriel Fernandes, Renan Maneli Mezabarba, Vinicius de Oliveira Rodrigues
We prove that, in Zermelo--Fraenkel set theory with the axiom of Foundation removed, the statement that every vector space has a basis implies the Axiom of Choice (),…
Menger and Rothberger games on convergence spaces
Renan Maneli Mezabarba, Rodrigo Santos Monteiro
We introduce Menger and Rothberger selection principles and games for convergence spaces. Alice plays families that meet every convergent filter, and Bob's selections are required…
On convergence structures in graphs
Paulo Magalhães Junior, Renan Maneli Mezabarba, Rodrigo Santos Monteiro
A closure operator on a set is a function satisfying, for all , the following properties: extensivity, $A \subseteq \op…
Pasting and stability in convergence spaces
Renan Maneli Mezabarba, Rodrigo Santos Monteiro, Thales Fernando Vilamaior Paiva
We prove a pasting lemma for locally finite closed covers of convergence spaces with limit codomains. We also show how the validity of such lemmas characterizes limit spaces.
Pointless proofs of the Menger and Rothberger games
Renan Maneli Mezabarba
This work presents proofs for Hurewicz's and Pawlikowski's Theorems about topological games in the context of lattices, in which one cannot argue with points.
A characterization of productive cellularity
Renan Maneli Mezabarba, Leandro Fiorini Aurichi, Lucia Renato Junqueira
We investigate the notion of productive cellularity of arbitrary posets and topological spaces. Particularly, by working with families of antichains ordered with reverse inclusion,…
Bornologies and filters in selection principles on function spaces
Leandro Fiorini Aurichi, Renan Maneli Mezabarba
We extend known results of selection principles in -theory to the context of spaces of the form , where is a bornology on . Particularly,…
Productively countably tight spaces of the form C_k(X)
Leandro Fiorini Aurichi, Renan Maneli Mezabarba
Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology…